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Questions and Answers
What is the intensity at $t = 1$ to the nearest hundredth?
What is the intensity at $t = 1$ to the nearest hundredth?
What is the maximum intensity of affection?
What is the maximum intensity of affection?
What is the amplitude of his love affection?
What is the amplitude of his love affection?
What is the period of his affection?
What is the period of his affection?
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What is the mean level of his affection?
What is the mean level of his affection?
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Study Notes
Word Problems Involving Sine or Cosine Functions
- A periodic function has the form y(t) = a sin(bt + c) + d, where t ≥ 0.
- The mean level of a periodic function is the average value of the function over one period.
- The amplitude of a periodic function is the maximum deviation from the mean level.
- The period of a periodic function is the time taken to complete one cycle.
Finding the Function
- If the mean level is 10, amplitude is 5, period is π, and phase constant is 3, the function is y(t) = 5 sin(2t + 3) + 10.
- To find the maximum value of y, find the maximum value of the sine function (which is 1) and multiply it by the amplitude, then add the mean level.
Particle Motion
- The equation y = 4 sin(4πt - 6) + 7 represents an oscillatory motion.
- The period of this motion is 1/2.
- The mean level of this motion is 7.
- The phase constant is -6.
- The amplitude is 4.
- The angular velocity is 4π.
Velocity of a Particle
- The velocity of a particle is given by the equation v(t) = 3 sin(2πt - π) + 1.
- The maximum speed is 4.
- The minimum speed is 0.
- The velocity at t = 6 is 2.
Intensity of Sound
- The intensity of sound is given by the equation I = 5 cos(2πt/3 - π/2) + 55 dB.
- The amplitude of this sound is 5 dB.
- The maximum intensity heard is 60 dB.
- The minimum intensity heard is 50 dB.
Affection of a Boy
- The intensity of a boy's affection is modeled as L = 10 cos(πt/2 + π/2) + 5, where t is in hours.
- The intensity of his affection when he meets his girl at t = 1 is approximately 2.99.
- The intensity of his affection at t = 4 is approximately 15.
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Description
Test your understanding of solving word problems involving sine or cosine functions in the form f(x) = acos(bx+c) + d or f(x) = asin(bx+c)+d with this quiz. Practice applying these functions to real-world scenarios and improve your problem-solving skills.
